Abstract. In this note, it is proved that multiplier algebras of analytic reproducing kernel Hilbert spaces which are compatible with the action of the torus group possess Kraus' completely contractive approximation property (CCAP) and, consequently, have the Property $S_\sigma $. Our results apply in particular to the usual reproducing kernel Hilbert spaces on bounded symmetric domains.

AMS Subject Classification (1991): 46E22, 47B32, 47L45

Keyword(s): operator algebras, reproducing kernel Hilbert spaces, multipliers of reproducing kernel Hilbert spaces, approximation properties

Received July 11, 2008, and in revised form October 11, 2008. (Registered under 6433/2009.)